Answer
Positive.
Work Step by Step
$-90^{\circ}\lt\theta\lt 90^{\circ}\implies90^{\circ}\gt-\theta\gt -90^{\circ}$
(Because we multiplied the inequality by a negative number, we flipped the inequality sign.)
$\implies -90^{\circ}\lt-\theta\lt90^{\circ}$
Secant function is positive as the angle $-\theta$ is in between $-90^{\circ}$ and $90^{\circ}$( This interval includes first and fourth quadrants. In these quadrants, secant function is positive ).
